The Labour party has challenged Britain's most senior civil servant to explain his role in the publication of a set of principles governing the role of the Tories' chief election strategist, which have been used to reject an inquiry into Lynton Crosby.

The shadow Cabinet Office minister, Jon Trickett, has warned Sir Jeremy Heywood that the "principles of engagement", hastily drawn up in recent days as Crosby faced questions about his business interests, may be "unenforceable and worthless".

Trickett wrote to Heywood after the cabinet secretary rejected Labour's call for an inquiry to examine a potential conflict between Crosby's business interests and his Tory party role on the grounds that a set of principles had been drawn up.

The Conservative party admitted that the "principles of engagement" were drawn up in recent days.

In his letter to Heywood, Trickett wrote: "Thank you for passing on 'the principles of engagement between Lynton Crosby and the Conservative party' – which are undated … It therefore appears that this was not properly drawn up by civil servants in order to avoid conflicts of interest in government, but hastily cobbled together after Mr Crosby had become a political embarrassment to the Conservative party."

Trickett then asked Heywood to answer a series of questions about the principles. He asked:

• Were you or any civil servants involved in any way in the drawing up of the terms of engagement published yesterday?

• Did you know that the principles of engagement which you sent me had only been 'written down in the last couple of days'?

• Did you know about them before this week, and when did you first see them?

• Do you have any evidence at all that these principles have been followed?

• Are you personally satisfied that Lynton Crosby has had no discussions with the prime minister or other ministers about tobacco policy, alcohol policy, NHS policy or fracking policy?

• Are you personally satisfied that there is no possibility of a conflict of interests between Mr Crosby's roles as an adviser to the Conservative party and an adviser to commercial organisations?

• Do you know who Mr Crosby's commercial clients are, and in the interests of transparency will you ensure that a full list is published immediately?

Crosby has faced questions over his business interests after it emerged that his company advises the tobacco group Philip Morris International. David Cameron recently announced that the government would be shelving plans to introduce plain cigarette packaging, in the face of strong lobbying by the tobacco industry.

The "principles of engagement" document released by Heywood says that in order to avoid a conflict of interest between Cameron's role as prime minister and Crosby's business interests a series of principles were agreed. These include an assurance from Crosby that he would not use his position as an adviser to the Tories to further his private business interests and he would not use his access to ministers to lobby for changes to government policy on behalf of clients.

In his letter Trickett questioned the value of the principles because Downing Street and the Tory chairman, Grant Shapps, have suggested they do not know the identity of Crosby's clients.

He wrote to Heywood: "Clearly, if the prime minister and the Conservative party are unaware of who Mr Crosby's clients are – which is what the chairman of the Conservative party says is the case – then you will agree that the principles of engagement are unenforceable and worthless. In the interests of transparency Mr Crosby's company's full client list should be published immediately."

The row came after Crosby said on Tuesday that he had never had any conversation with the prime minister or the health secretary about tobacco. In a statement issued by his firm, CTF Partners, Crosby said: "At no time have I had any conversation with or lobbied the prime minister, or indeed the health secretary or the health minister, on plain packaging or tobacco issues. Indeed, any claim that I have sought to improperly use my position as campaign adviser to the Conservative party is simply false."